Suppose a market’s demand and supply curves take on the following characteristic

Question

Suppose a market’s demand and supply curves take on the following characteristics:

QD = 100 – 2.5(P) + 0.95(Y – T) QS = 2(P)

where:
QD quantity demanded
QS quantity supplied
P price of the commodity Y personal income
T personal taxes

Given the above model, please answer the following questions:

1.What is the market-clearing price and quantity if personal taxes (T) equal zero and personal income (Y) is $400?

2. Suppose a personal tax rate of 20 percent is introduced.

What is the impact on the market equilibrium price and quantity?

What is the tax revenue received by the government?

How much did total revenue received by producers change?

How much did total expenditures by consumers change?

3. Suppose personal income rose by 10 percent. Using the tax rate of 20 percent introduced in question 2 above,

What is the impact on the equilibrium price and quantity

previously calculated in question 2?

What is the income elasticity of demand? What does this

calculated elasticity indicate about this product?

4. If we added the real wealth term “+0.01(W)” to the demand equation, how much would your answer change in question 1 (price and quantity) if the level of real wealth was $3,000 (i.e., W = 3,000)? Draw a graph depicting the effects this has upon market equilibrium compared to your answer to part 1.

Explanation / Answer

(1)

Plugging in given values,

QD = 100 - 2.5P + 0.95 x (400 - 0) = 100 - 2.5P + 380

QD = 480 - 2.5P

Equating with QS,

480 - 2.5P = 2P

4.5P = 480

P = 106.67

Q = 2 x 106.67 = 213.34

(2) In this case, T = tY = 0.2Y, therefore Y - T = Y - 0.2Y = 0.8Y = 0.8 x 400 = 320

(a) QD = 100 - 2.5P + 0.95 x 320 = 100 - 2.5P + 304 = 404 - 2.5P

Equating new QD with QS,

404 - 2.5P = 2P

4.5P = 404

P = 89.78

Therefore, price decreases by (106.67 - 89.78) = 16.89

Q = 2 x 89.78 = 179.56

Therefore, quantity decreases by (213.34 - 179.56) = 33.78.

(b) Tax revenue = tY = 0.2 x 400 = 80

(c) Since the tax is imposed on consumer income, revenue received by producers will be equal to the total expenditure by consumers, both being equal to (Price x Quantity).

Before tax, Revenue received by producers = 106.67 x 213.34 = 22,756.98

After tax, Revenue received by producers = 89.78 x 179.56 = 16,120.90

Revenue received by producers decreases by (22,756.98 - 16,120.90) = 6,636.08

(d) As explained above, therefore, total expenditure of consumers decreases by 6,636.08.

NOTE: As per Answering Policy, first 2 sub-parts with multiple parts have been answered.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.